Question

Two zeros of `f(x)=x^3-6x^2-16x+96` are `4` and `-4`. Why must the third zero be a real number?

Answer 1

When the polynomial has real coefficients, the complex roots must appear as conjugates, to preserve their coefficient realness. So an odd polynomial necessarily must have a real root.

Explanation:

When the polynomial has real coeficients, the complex roots must appear as conjugates, to preserve the coefficient's realness. So an odd polynomial necessarily must have a real root.